Both
Except for July and August the museum is free on the first Tuesday of every month. In Sept it's free every Tuesday. The museum recommends that you reserve your tickets on these days because of the amount of people who go and also to skip long lines getting in.
You can pay on the site.
You totally could pay in person.
You can pay in person but some of the extras may be sold out.
I think you can do that.
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